Hilbert-Schmidt distance to the closest separable state: A simple algorithm

Zapraszamy w piatek 04.02.2022r. o godz. 12:15

Seminarium ONLINE  pt.: Hilbert-Schmidt distance to the closest separable state: A simple algorithm. Speaker: mgr Palash Pandya, Affiliation: University of Gdańsk

Place:https://zoom.us/j/94361414308?pwd=cC8xaTNBd290Rzk1TUgrZzZhcWczUT09

Abstract:Gilbert proposed an iterative algorithm for bounding the distance between a given point and a convex set. We apply the Gilbert's algorithm with a few modifications and simplifications to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert-Schmidt distance does not form a proper entanglement measure, it can nevertheless be used as a very robust indicator of the amount of entanglement. We provide a few methods based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outputs successively improved approximations to the closest separable state for the given state. We show that the approximate closest separable states are then used in constructing Entanglement Witnesses (EW) that are close to optimal. We demonstrate the efficacy of the method with examples. The flexibility of the algorithm enables a study of the boundary of the sets of separable (biseparable, etc) states as well as the construction of EWs in a Hilbert space of arbitrary dimension